Thursday, 23 June 2016

Gun Fusion: Two barrels to the stars

To start a fusion reaction, you have to create extreme conditions. A combination of stellar temperatures, incredible pressures and lightning-quick energy dumps have all been tried to create these conditions, with varying degrees of success.

Nuclear fusion, as you may already know, is the addition of two atomic nuclei to create products with a slightly lower mass. The difference in mass is released as energy.

A view inside a Tokamak. The pink rink is the plasma.

If you've sat through basic chemistry, you'll know that atoms contains electrons, protons and neutrons. Two of these are charged - they act through electromagnetic forces to repel or attract each other.

You will therefore realize that trying to push two nuclei full of positively-charged protons together so that they can fuse means trying to overcome the electromagnetic forces keeping them apart.

The nuclear force and the coulomb barrier.

These forces, on an atomic scale, are measure in electron-volts. The energies discussed here are on the mega-electron-volt scale, or MeV.

Defeating the electromagnetic repulsion in practice means giving each fusing atom large amounts of energy.

For example, the easiest fusion reaction to achieve, between Deuterium and Tritium, requires a temperature of about 40 million K.

Current methods and applications of spacecraft

As mentioned, several methods have been used to ignite fusion already.

The most commonly discussed, and the subject of large-scale, multi-billion dollar experimentation, are magnetic confinement and inertial containment.

The magnetic confinement method relies on very large electromagnets generating incredibly powerful magnetic fields to contain an ionized fusion fuel plasma. They are necessary as like any gas, heating the plasma increases its pressure. Heating it to multi-million Kelvin temperatures generates incredible pressures, which have to be countered with equal force by the magnetic fields. Examples of this approach are the Tokamak and the Wendelstein 7-X Stellarator.

The inertial containment method attempts to bypass the requirement of containing the plasma by working on extremely short timescales. A zap of energy is delivered very very quickly, in the form of a laser or ion beam, to a frozen ball of fusion fuel. The ball's exterior vaporizes and expands, thereby pushing against the ball's interior. If done properly, the compression and heating of the interior is sufficient to ignite a fusion reaction before the whole thing explodes.

As a result of their popularity, they are featured heavily in both science fiction and in real-world fusion designs.

The focus of this blog is space and spaceships, and naturally, we must consider the myriad proposals for fusion-driven spaceships.

Fusion is an excellent choice for propelling spacecraft. It is much more powerful than chemical fuels, but does not have the rare fuels and radioactive residues of fission. However, the disadvantages of using fusion with the aforementioned methods are equal in measure to its disadvantages.

A magnetic containment fusion spacecraft has to carry the mass of huge electromagnets and their cooling equipment. It has to power both with a continuous, powerful energy source, which might mean another nuclear reactor. Furthermore, it has to find a way to extract the energy from the reactor and apply it to the propellant. This can be done by extracting the heat from the reactor walls indirectly, with associated conversion losses, or pumping propellant into the reaction chamber and risking the plasma being destabilized.

Inertial confinement is better suited to propelling spacecraft, but has its own complication. It requires petawatt lasers or a particle accelerator, with their associated mass. They have to be powered by capacitors, which are notoriously low on energy density. A fusion pellet can easily be placed inside a cloud of propellant for propulsion, but the challenge becomes transmitting the energy pulse through the propellant and onto the pellet without losses or deviation. The entire ignition process also has to maintain a degree of precision even when under acceleration and or when subject to external bumps.

So, fusion spacecraft have large mass overheads, require significant external energy input, and have various difficulties when it comes to using fusion energies for propulsion.

Gun fusion

What is proposed here is a method to ignite fusion using well-understood technologies, requiring only minimal power inputs yet remaining well adapted for use in propulsion.

Gun-fusion configuration

The design is composed of two railguns, each accelerating a specially configured bullet, to be launched at each other with the intention of igniting fusion within a solid propellant cylinder. It involves a 5 step process:

-Launch.

The bullets contain three elements: a thin (100nm) faceplate of gold, a chamber containing a gas mixture of deuterium, tritium and hydrogen, and a solid 'tail'. They are launched using a railgun to velocities of 20-100km/s depending on configuration.

The basic bullet configuration

-Impact.

Upon impact, the gold faceplates vaporize as kinetic energy is converted into thermal energy (10% efficiency). The heat radiated by the impact raises the temperature of the gas mixture (1% of bullet mass) to 3.125 million K. This lowers pressure requirements for ignition by a factor of 100000.

The impact takes place under a half-sphere of polyethylene or other suitable propellant. The energy released by the fusion reaction vaporizes and ionizes the propellant. The momentum of the propellant is captured by electromagnetic or mechanical means.

Configuration for gun-fusion drive

This 'gun' fusion has several clear advantages over the aforementioned methods of igniting fusion.

Railguns are simpler than electromagnets cooled to superconducting temperatures or petawatt lasers using heavy, bulky supercapacitors. While the total energy involved is equal to or greater than that of inertial confinement fusion, the power levels are much lower and vastly more manageable. The fusion fuel does not have to be handled at cryogenic temperatures either.

With today's technologies, railguns are lighter than particle accelerators or Tokamaks. They are also more efficient than petawatt lasers, and the fusion mechanic is more robust. In the special designs discussed below, they can be replaced by even lighter methods of accelerating the bullets.

Another important characteristic for fusion propulsion is that the fusion equipment can be placed arbitrarily far away from where the fuel is ignited. This lowers shielding requirements.

Worked example

We will start with a payload mass, a mission and then go from there to work out a spaceship design.

We'll assume a 100 ton mission to Mars. The mission is an impulse trajectory requiring 100km/s of deltaV and crossing a 54.6 million km distance is about 12 days.

Deuterium-Tritium fusion products.

To stick close to the findings of the cited research, we will be using D-T fuel. 20% of the energy is released as soft X-rays, with the remainder in 14MeV neutrons. It is therefore essential to capture the neutron's energy. For this reason, polyethylene is the propellant of choice. It is light, and absorbs over 98% of neutrons within 4cm depth. A 4cm radius hemisphere has a volume of 134cm^3 and a mass of 128 grams.

Polyethylene has p: 0.96g/cm^3, A: 28g/mol

Let's say we ignite 0.1g of deuterium/tritium fuel, within two 10g bullets, with a fuel burn-up of 6.6% (we need 3g/cm^2 for 33%, but we're using a sphere of room-temperature deuterium/tritium at 0.2g/cm^3).

We obtain 4.5GJ per impact-fusion.

The fusion products are released in a spherical fireball, so about 50% reach the polyethylene half-sphere. 98% of neutrons are absorbed, 100% of X-rays too. It is safe to say that 50% of the energy released is used to heat the polyethylene.

The polyethylene gains 2.3GJ. It has a heat capacity of 1.25J/g/K, so it rises to a temperature of 14 million K. Using the average molecular kinetic energy equation, we reach a particle velocity of 111.7km/s. We obtain 35kN of thrust, depending on the efficiency of the electromagnetic nozzle, assumed to be 85%.

The Mini-Mag Orion, which uses a similar propulsion system to our worked example spaceship

Accelerating 10g bullets to 20km/s (staged compression) requires 2MJ. A 16% efficient railgun would require 10MJ. If we include a heatsink, this figure rises.

If the spacecraft uses an electromagnetic system for capturing momentum from the polyethylene particles, then we might use a 20% efficient MHD generator. It would produce 460MJ per pulse, more than enough to power two railguns. A simpler thermoelectric generator with 5% efficiency still produces a sufficient 115MJ. The latter can be integrated into the radiation shielding on the railguns.

How a thermoelectric generator works

400MJ can be contained in 4 tons of supercapacitors, for two cold re-starts. The current-generation 64MJ railgun masses 67 tons (including capacitors). We can extrapolate that two 10MJ railguns might mass 20 tons.

The ICAN-II spacecraft places engine mass at 27 tons to handle an output of 11.7GW. If the gun-fusion is fired once per second, power output is 2.3GW, so an extrapolated figure of 5.3 tons might be appropriate to cover the electromagnetic particle capture system.

The mass of the polyethylene propellant ejection system should be insignificant (less than 1 ton). Structural mass is roughly estimated at 10% of dry mass, so approximately 12.9 tons. This includes suspension for the nozzle, to smooth out accelerations.

Final specifications:

Payload: 100 tons

Drive system: 29.3 tons

Structural mass: 12.9 tons

Drive power: 2.3GW (fusion), 1.96GW (nozzle).

Exhaust velocity: 111km/s

Thrust: 35kN

Firing rate: 1Hz

Mass flow: 148g/sec (of which 128g/sec is propellant).

DeltaV: 100km/s

Consumables mass: 53.8 tons (711TJ mission energy/1.955GJ per impact)

Total mass: 196 tons

In short, a small, simple-to-construct spaceship can reach Mars in under a month.

Future improvements:

The design mentioned in the 'Gun fusion' section requires that the bullets impact at 100km/s. In fact, studies on impact fusion typically recommend velocities approaching 1000km/s, where a microgram pellet of fuel is compressed in one dimension against an immobile target. The solution to vastly reducing velocity and energy requirements is staged compression.

Each stage compresses and heat the gas in the following stages. With a sufficient number of stages, the fuel bubble can achieve ignition temperatures and pressures at velocities of only 20km/s.

Another 'improvement' is the use of various acceleration mechanisms. A two-staged light gas gun could theoretically achieve the necessary velocities by adding a third stage. A coilgun can be used, with improvements in efficiency. It also be made circular to make a more compact accelerator.

Ablative propulsion has been proposed. A laser or ion beam vaporizes the tail of the bullet, accelerating it. It would be very useful if efficiencies rise. Their greatest advantage is gradual acceleration: the bullet can be accelerated up to the point of impact. However, they would require unobstructed line of sight and any fault in the laser's accuracy or the ablative material's manufacture will cause the bullets to miss.

A final improvement is the magnetic manipulation of the bullets. By making the bullets' tails out of a ferromagnetic material such as iron, their trajectory can be modified and corrected by magnetic forces. This would allow accurate impacts from further away (important for very large spaceships using larger yields) or off-angle acceleration of the bullets.

Could off-angle magnetic accelerators be positioned in such a way that the majority of the accelerators are not pointing directly at each other? (potentially reducing risks of misses and engine damage, as well as allowing long accelerators too be put into an easily-stackable spine)

Could this method be adapted in any way for terrestrial civilian powerplants?

I think the perpendicular arrangement is the simplest and has the lowest energy requirements. An off-angle accelerator would have to produce enough lateral velocity to obtain the necessary perpendicular momentum. At extreme angles (such as 80 degrees), the bullets would have to be accelerated to velocities as great as 113km/s. On top of that, it would have to deal with the 'tails' pushing in at a slanted angle to compress the working fluid (gas mixture). I can't imagine a diagonal piston working very well.

No, I think the best way to do it using a spinal accelerator is using a fixed target. Accelerate the bullet to 40km/s, and gently position a slow-moving plate in its path.

The patent described a bullet design where inverted cones would 'scoop up' fuel gas and compress it inside a cloud of propellant. This would be easy to set up for a power plant. The only difficulty would be dealing with pulsed operation: the detonation would blow away surrounding fuel.

Another way to avoid the "railguns shooting each other if one fails to fire" problem might be to use three instead - though I am not sure how well three projectiles colliding would compress the fusion fuel, and of course making three guns fire exactly at the same time is about three times (three distinct pairs) as hard as making two guns fire exactly at the same time.

Very interesting, I notice some similarities with the magneto-inertial approach (https://www.nasa.gov/pdf/716077main_Slough_2011_PhI_Fusion_Rocket.pdf). How would you compare the two? Is gun fusion more easily achieved in the near term?

That's a very interesting article. Collapsing a metal ball onto a fusion fuel pellet sounds more like the z-pinch than the kinetic impact fusion method.

I see the article's method as being more efficient (low megajoules required) and leading to higher propulsion efficiency. It would also have the benefit of using smaller pulse units, meaning smoother acceleration, lower structural mass and less suspension mass.

However, producing large magnetic fields means using large, complicated, heavy and bulky magnets with superconducting systems that bring along complex cryogenic cooling systems and more. There is an enormous mass penalty. Kinetic accelerators, especially potential third-generation chemical accelerators, will be vastly more mass-efficient and at the end the day, simpler and more robust.

I think an appropriate analogy would be the difference between a nuclear power plant's ultra-efficient but humungous triple-expansion steam turbines, to the less efficient but much simpler and quicker race car engine. They could prossibly be developed side-by-side, but for different purposes and reasons.

"A spherical array of minirailgun plasma accelerators is a potential driver for forming imploding spherical plasma liners that can reach HEDP-relevant ( about 0.1 Mbar) pressures upon stagnation. The liners would be formed via merging of 30 or more dense, high Mach number plasma jets (n about 10^16−17 cm−3, M about 10–35, v about 50–70 km/s, rjet about 5 cm) in a spherically convergent geometry. The small (typically 1-2 cm square bore x 15-50 cm length) parallel-plate railguns with ceramic insulators would use pulsed injection of high-Z gas at the breech via fast opening valves to produce high density plasma jets with velocity in the 50-100 km/s range. Recent tests at HyperV using a single pulsed capillary discharge injecting into the minirailgun breech have achieved plasma densities in the bore approaching 10^18 cm−3, with densities in the jet plume exceeding 1017 cm−3 at velocities above 50 km/s. Total plasma jet mass in these 1 cm square bore tests has not yet been determined, but similar tests of an earlier 6 mm square bore 13 cm long device, with a roughly 3 μs, 100 kA current pulse using an aluminized mylar fuse starting from rest, yielded 90 μg of plasma at 50 km/s, and about 40 μg at 63 km/s. A modest scaleup of the railgun to a 2 cm square bore operating at longer pulse widths of 200-300 kA should be capable of accelerating a few thousand micrograms of high-Z gas (e.g. xenon) to above 50 km/s. This performance should be sufficient for reaching HEDP-relevant pressures."

The overall thrust would be to make the entire device smaller and more "user friendly" (no risk of the railguns becoming misaligned and shooting solid projectiles across the reaction chamber and into the other wall at 100+ Km/sec). Scaling down the fusion reactor's size and mass is always good, since the performance of the ship will be improved more by the reduction in mass than almost anything else.

And during operation, the crew can "switch gears" by injecting water into the exhaust stream to trade ISP for thrust during combat manoeuvres.

Quite an interesting alternative. The ammunition cannot be damaged, and it will be lighter. Firing rates might be higher too, as less energy is expended accelerating the fusion fuel.

However, while I agree that the consequences of an accident will be minimal, the set is more fragile. Higher velocities mean that smaller angular deviations are needed to result in large deviations from target. Unlike a solid compressor, plasma would not have the ability to self-correct the angle of impact or absorb minor misalignments.

As for switching gears, I believe it comes with a 30% loss in efficiency.

Switching gears is trading efficiency for thrust, so for a spaceship commander needing to sidestep a missile or doing a burn to enter or break out of an orbit.

The real issue is "every gram counts", so any means to reduce the mass of a spaceship will be eagerly sought after. I am also eager to see this come to fruition because of the benefits here on Earth. Having compact power sources not only would make living in cities and towns cheaper, cleaner and easier, but compact power plants like that could also revolutionize sea and air travel as well.

Again, thank you for posting this sort of thing. I've been racking my brain over the last few years trying to decide the best (or least bad) method of fusion propulsion for my novel's warships. I began with D-He3 and moved on to boron after reading that that seriously high powered lasers at super high firing rates had be hypothesized to be able to do the job. But the whole set up is very easy to damage and difficult to shield. I'm kind of at the fatigue point where I gloss over some of the harder numbers and finer details, because we just don't know what will really work. :/

A good 'rule of thumb' for describing technologies in fiction is: is it important for the plot?

What I mean by this, is that there are very little situations where the specific type of technology is specifically mentioned unless it pertains to a plot point.

Imagine yourself talking to a friend about an awesome new car. It has a type of engine, a horsepower and a power-to-weight ratio... but do you discuss fuel consumption per kW? Do you talk about the fact that it is an Four-Cycle Internal Combustion Otto cycle chemical engine running on hydrocarbon fuels extracted in Saudia Arabia, shipped by Teekay Corp to be refined in Texas, USA?

No, you just say 'engine' or 'V6' or even brand names like 'Hemi', and your friend understands.

The same goes for most technological things we interact with, and realistic characters do the same. It's an 'iPhone' with '4G', not a handheld advanced telecommunications, data processing and entertainment device with tactile screen and 2W antenna!

So, if you're trying to understand the finer details of fusion, just start off picturing yourself as a character in your setting talking to someone else about that piece of technology realistically. It's a 'fusion' engine, yeah, but people will think the amount of thrust or the radiated gigawatts is more important. Or maybe they'll just call it a 'General Atomics Mark II' and everyone will understand.

@Matter Beam "A good 'rule of thumb' for describing technologies in fiction is: is it important for the plot?"

I tend to agree. What I like to do is sprinkle in a few paragraphs of description here and there about what is being used. I like it when I see that in other writers like Thomas Clancy, John Lumpkin, or Michael Creighton. It can easily be overdone and I've found myself chopping off